There are two types of memory on the iPhone and iPod touch: Storage memory and RAM. If you download a lot of music and videos and install a lot of third-party apps, you can run low of storage memory, especially on the 8 GB devices. One of the things you can do is to delete third-party apps, music, and videos when you are no longer using them.
Both devices have 128 MB of RAM, which is used to run the OS and applications. Some users have complained of slowdowns and other problems associated with not enough RAM. Fortunately, the iPhone and iPod touch will warn you if you are low on memory. If you receive one of these warnings asking you to do something, do it immediately—don’t put it off. Also, if you’re finished with an app, close it down completely. With the app displayed, press AND HOLD DOWN the Home key. This will close it down and take you to the Home screen.
Finally, you might consider investing in a third-party app that will help you manage the memory on your device. A number are available on the App Store, including iStat ($1.99), Free Memory ($0.99), and Memory Status ($0.99).